Existing research on the European Union's (EU) multilevel parliamentary system builds on the hypothesis of parallel evolution, situating explanations for European Parliament (EP) empowerment at the EU level and explanations for national parliamentary powers in EU affairs at the national level. We propose the hypothesis of co-evolution, which specifies a connection between national and European arenas of parliamentarization. We study whether the EP's empowerment enhances or reduces pressure on national parliaments to strengthen their own EU-related competences. First, we argue that national parliamentary parties take conscious positions on the powers of the EP. Second, support for the EP among the party composition of national parliaments tells us whether parliaments regard the EP as a competitor or ally, feeling pressed, or relieved of the pressure, to strengthen their EU-related competences.